Math Is Fun Forum

Douglasm

Member

Registered: 2009-12-25

Posts: 15

Can anyone help me with this summation?

I don't know how to deal with these products in the summation. Any assistance is welcome!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Can anyone help me with this summation?

Hi Douglasm;

I am assuming you sum looks like this:

Just some guidelines. Sums are like integrals, very few have closed forms in terms of elementary functions. Harder for sums because there a less tables available for them.

I have searched through my tables and given the sum over to Mathematica and Maple. They can do the sum but not in terms of elementary functions.

What can a person do. There are 2 attempts for a combinatoric sum like that. A combinatoric argument like block walking which allows us to restate the sum as a combinatorics problem that we know the answer to. I am not seeing that here.

You can use the one available human method put together by Wilf and Zeilberger called the snake oil method. Unfortunately I no longer remember how to even started with that method but it is explained in the book Generatingfunctionology by Herbert S. Wilf. It is free on the internet to download as are all of Zeilberger's and Wilf's books.

Sorry I couldn't do a little bit more, if you look at the method and try it on the problem and get stuck, then post where you are stuck. It might jar my memory of the method.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Douglasm

Member

Registered: 2009-12-25

Posts: 15

Re: Can anyone help me with this summation?

Thanks bobbym. I already have this book (didn't read it yet though). I'm also using Andreescu's book of combinatorics. I'll try to find a method for solving such summations in those books. This question looks harder than it should be...it is in a high school level book. I forgot to post the answer:

(maybe looking at the answer will refresh your memory =P)

Last edited by Douglasm (2010-02-23 09:40:33)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Can anyone help me with this summation?

Hi Douglasm;

The problem I think is that your notation your using is upside down. That's what threw me.

Your answer

is commonly read:

(n-2) objects taken 2n at a time. Since 2n  > n-2 for all n>=0 your answer equals 0. Normally you see it written like this.

Same thing goes for the series. Can you tell me what book that series came from?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Douglasm

Member

Registered: 2009-12-25

Posts: 15

Re: Can anyone help me with this summation?

You're right. This answer doesn't make much sense, but it is writen like that in the answers section. Probably it is a typo. The book is Augusto Morgado's "Análise Combinatória e Probabilidade", it's a brazilian one. I'm starting to get tired of this book actually, it doesn't help me too much.